To perform the tensile test on the given samples and to determine the associated properties of
specimens using universal testing machine.
Universal testing machine
Given specimens (cast iron and aluminium)
Mechanical testing plays an important role in evaluating fundamental properties of engineering
materials as well as in developing new materials and in controlling the quality of materials for
use in design and construction. If a material is to be used as part of an engineering structure
that will be subjected to a load, it is important to know that the material is strong enough and
rigid enough to withstand the loads that it will experience in service. As a result engineers have
developed a number of experimental techniques for mechanical testing of engineering materials
subjected to tension, compression, bending or torsion loading.
Tensile properties indicate how the material will react to forces being applied in tension. A
tensile test is a fundamental mechanical test where a carefully prepared specimen is loaded in
a very controlled manner while measuring the applied load and the elongation of the specimen
over some distance. Tensile tests are used to determine the modulus of elasticity, elastic limit,
elongation, proportional limit, reduction in area, tensile strength, yield point, yield strength and
other tensile properties.
The most common type of test used to measure the mechanical properties of a material is the
Tension Test. The main product of a tensile test is a load versus elongation curve which is then
converted into a stress versus strain curve. Since both the engineering stress and the engineering
strain are obtained by dividing the load and elongation by constant values (specimen geometry
information), the load-elongation curve will have the same shape as the engineering stressstrain curve. The stress-strain curve relates the applied stress to the resulting strain and each
material has its own unique stress-strain curve. A typical engineering stress-strain curve is
shown below. If the true stress, based on the actual cross-sectional area of the specimen, is
used, it is found that the stress-strain curve increases continuously up to fracture.
Stress = s = P/A (Load/Initial cross-sectional area)
Strain = e = ∆L/L (Elongation/Initial gage length)
Engineering stress and strain are independent of the geometry of the specimen. In start stress
and strain are in linear relationship.
This is the linear-elastic portion of the curve and it indicates that no plastic deformation has
occurred. In this region of the curve, when the stress is reduced, the material will return to its
In this linear region, the line obeys the relationship defined as Hooke's Law where the ratio of
stress to strain is a constant.
σ = Ee
σ = engineering stress
e = engineering strain
E = elastic modulus or young’s modulus
The slope of the line in this region where stress is proportional to strain and is called the
“modulus of elasticity” or “Young's modulus”. The modulus of elasticity (E) defines the
properties of a material as it undergoes stress, deforms, and then returns to its original shape
after the stress is removed. It is a measure of the stiffness of a given material
The part of the stress-strain diagram after the yielding point. At the yielding point, the plastic
deformation starts. Plastic deformation is permanent. At the maximum point of the stress-strain
diagram (σ UTS), necking starts.
In ductile materials, at some point, the stress-strain curve deviates from the straight-line
relationship and Law no longer applies as the strain increases faster than the stress. From this
point on in the tensile test, some permanent deformation occurs in the specimen and the
material is said to react plastically to any further increase in load or stress. The material will
not return to its original, unstressed condition when the load is removed. In brittle materials,
little or no plastic deformation occurs and the material fractures near the end of the linearelastic portion of the curve.
For most engineering design and specification applications, the yield strength is used. The yield
strength is defined as the stress required to produce a small, amount of plastic deformation.
The offset yield strength is the stress corresponding to the intersection of the stress-strain curve
and a line parallel to the elastic part of the curve offset by a specified strain (in the US the offset
is typically 0.2% for metals and 2% for plastics while in UK offset method is 0.1% or 0.5%.
Stress corresponding to 0.1% strain is known as proof strength).
In some materials there is upper yield point and lower yield point. In these materials load at
yield point suddenly drops this is known as yield point. After decreasing load, strain increases
while load remain almost constant. This phenomena is known as yield-point elongation. After
yielding stress increases. The deformation occurring throughout the yield-point elongation is
heterogeneous. At the upper yield point, a discrete band of deformed metal, often readily
visible, appears at a stress concentration, such as a fillet. Coincident with the formation of the
band, the load drops to the lower yield point. The band then propagates along the length of the
specimen, causing the yield-point elongation.
Figure 1: yield elongation phenomena in material by
volume 8 - Mechanical Testing and Evaluation ASM hand book
Figure 2: Upper and lower yield point in material by ASM hand book
volume8 - Mechanical Testing And Evaluation
A similar behaviour occurs with some polymers and superplastic metal alloys, where a neck
forms but grows in a stable manner, with material being fed into the necked region from the
thicker adjacent regions. This type of deformation in polymers is called “drawing”.
Ultimate Tensile Strength
The ultimate tensile strength (UTS) or, more simply, the tensile strength, is the maximum
engineering stress level reached in a tension test. The strength of a material is its ability to
withstand external forces without breaking. In brittle materials, the UTS will at the end of the
linear-elastic portion of the stress-strain curve or close to the elastic limit. In ductile materials,
the UTS will be well outside of the elastic portion into the plastic portion of the stress-strain
Measures of Ductility
The ductility of a material is a measure of the extent to which a material will deform before
fracture. The amount of ductility is an important factor when considering forming operations
such as rolling and extrusion. It also provides an indication of how visible overload damage to
a component might become before the component fractures.
In general, measurements of ductility are of interest in three ways:
1. To indicate the extent to which a metal can be deformed without fracture in
metalworking operations such as rolling and extrusion.
2. To indicate to the designer, in a general way, the ability of the metal to flow plastically
3. To serve as an indicator of changes in impurity level or processing conditions. Ductility
measurements may be specified to assess material quality even though no direct
relationship exists between the ductility measurement and performance in service.
The conventional measures of ductility are the engineering strain at fracture (usually called the
elongation) and the reduction of area at fracture. Both of these properties are obtained by fitting
the specimen back together after fracture and measuring the change in length and crosssectional area.
% elongation =
Where Lf = final length
Lo = initial length
% Reduction in area =
Where Ao = initial length
Af = final length
Resilience is the capacity of a material to absorb energy when it is deformed elastically and
then, upon unloading, to have this energy recovered. The associated property is the modulus of
resilience, Ur which is the strain energy per unit volume required to stress a material from an
unloaded state up to the point of yielding
Ur = ∫ σdx
Assuming a linear elastic region,
Ur = ½ σyƐy
Toughness is a mechanical term that may be used in several contexts. For one, toughness (or
more specifically, fracture toughness) is a property that is indicative of a material’s resistance
to fracture when a crack (or other stress-concentrating defect) is present. Because it is nearly
impossible (as well as costly) to manufacture materials with zero defects (or to prevent damage
during service), fracture toughness is a major consideration for all structural materials.
Another way of defining toughness is as the ability of a material to absorb energy and
plastically deform before fracturing.
For dynamic (high strain rate) loading conditions and when a notch (or point of stress
concentration) is present, notch toughness is assessed by using an impact test.
Several mathematical approximations for the area under the stress-strain curve have been
For ductile metals that have a stress-strain curve like that of the structural steel, the area under
the curve can be approximated by
For brittle materials, the stress-strain curve is sometimes assumed to be a parabola, and the
area under the curve is given by
Poisson’s ratio is defined as the negative of the ratio of the lateral strain to the axial
strain for a uniaxial stress state.
Only two of the elastic constants are independent so if two constants are known, the third can
be calculated using the following formula:
E = 2G (1 + v)
E = modulus of elasticity (Young's modulus)
V = Poisson's ratio
G = modulus of rigidity (shear modulus)
Up to maximum stress deformation is homogeneous and
material deform plastically. But after maximum stress
delocalized deformation takes place. After UTS stresses are
concentrated at weaker portion of the specimen and a neck is
formed at that there. Load bearing capacity of material
decrease due to necking. Up to the point at which the
maximum force occurs, the strain is uniform along the gage
length; that is, the strain is independent of the gage length.
Figure3: necking area in sample by AMS metal
handbook volume 8 - Mechanical Testing and
However, once necking begins, the gage length becomes very
Specimen for Tension Test
In standard tensile specimen normally,
the cross section is
rectangular specimens are also used. The
“dogbone” specimen configiration was
Figure4: standard specimen shape by AMS metal handbook volume 8 - Mechanical
Testing and Evaluation
deformation is confined to the narrow center region (which has uniform cross section along its
length) and also to reduce the likelihood of fracture at the end of the specimen.
The standard diameter is approximately
12.8 mm (0.5 in.), whereas the reduced
section length should be at least four
times this diameter; 60 mm is common.
Gauge length is used in ductility
computations, as discussed in Section
Figure5: dimension of standard specimen Materials Science and Engineering by D.
6.6; the standard value is 50 mm (2.0 in.)
Machine for Tension Test
According to the loading type, there are two kinds of tensile testing machines;
1) Screw Driven Testing Machine: During the experiment, elongation rate is kept constant.
2) Hydraulic Testing Machine: Keeps the loading rate constant. The loading rate can be
set depending on the desired time to fracture.
A tensile load is applied to the specimen until it fractures. During the test, the load required to
make a certain elongation on the material is recorded.
Put gage marks on the specimen
Measure the initial gage length and
Select a load scale to deform and fracture
the specimen. Note that that tensile strength
of the material type used has to be known
Record the maximum load
Conduct the test until fracture.
Measure the final gage length and diameter.
The diameter should be measured from the
Figure 6: specimen and machine arrangement for tension
test by AMS metal handbook volume 8 - Mechanical Testing and
For Aluminium specimen
Initial length of specimen = Lo = 100mm
Final length of specimen = Lf =
Final area of specimen = Af =
Yield strength = 85.59 kN
Ultimate tensile strength = 108.8731628
Fracture strength = 137.755N
Modulus of resilience =
Modulus of toughness =
For Cast Iron specimen
Initial length of specimen = Lo = 100mm
Final length of specimen = Lf = 68.5mm
Final area of specimen = Df =
Yield strength =
Ultimate tensile strength = 748.502994 kN
Fracture strength =
Modulus of resilience =
Modulus of toughness =
Application of Tension Test
Tensile testing is used to guarantee the quality of components, materials and finished products
within a wide range industries. Typical applications of tensile testing are highlighted in the
following sections on:
Electrical and Electronics Industry
Medical Device Industry
Paper and Board Industry
Plastics, Rubber and Elastomers Industry
Safety, Health, Fitness and Leisure Industry
Materials Science and Engineering by D. Callister
8 - Mechanical Testing and Evaluation
Mechanical metallurgy by Dieter